Objectives Simplify rational expressions Multiply and divide rational

Objectives Simplify rational expressions. Multiply and divide rational expressions.

Vocabulary rational expression

A rational expression is a quotient of two polynomials. Examples of rational expressions include the following:

Because rational expressions are ratios of polynomials, you can simplify them the same way as you simplify fractions. Recall that to write a fraction in simplest form, you can divide out common factors in the numerator and denominator. Caution! When identifying values for which a rational expression is undefined, identify the values of the variable that make the original denominator equal to 0.

Example 1 A: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. 10 x 8 6 x 4 510 x 8 – 4 5 x 4 Quotient of Powers Property = 3 36 The expression is undefined at x = 0 because this value of x makes 6 x 4 equal 0.

Example 1 B: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. x 2 + x – 2 x 2 + 2 x – 3 (x + 2)(x – 1) = (x + 2) (x – 1)(x + 3) Factor; then divide out common factors. The expression is undefined at x = 1 and x = – 3 because these values of x make the factors (x – 1) and (x + 3) equal 0.

Example 1 B Continued Check Substitute x = 1 and x = – 3 into the original expression. (1)2 + (1) – 2 0 = (1)2 + 2(1) – 3 0 (– 3)2 + (– 3) – 2 4 = (– 3)2 + 2(– 3) – 3 0 Both values of x result in division by 0, which is undefined.

Check It Out! Example 1 a Simplify. Identify any x-values for which the expression is undefined. 16 x 11 8 x 2 28 x 11 – 2 Quotient of Powers Property = 2 x 9 18 The expression is undefined at x = 0 because this value of x makes 8 x 2 equal 0.